1. The problem statement, all variables and given/known data
I am doing self-study. I am on problem 5.6 #27 in the Stewart text 3rd E.

I don't understand why the integration limits changed after the given substitution.

The given substitution was:

x=θ^2 dx=2θdθ

2. Relevant equations
Please see attachment.

3. The attempt at a solution

I understand the substitution, and how theta sq became 2theta d theta. What I don't understand is, why when the x was substituted, the integration limits changed from a square root to no square root.1. The problem statement, all variables and given/known data

The original limits of integration are from [itex]\theta= \sqrt{\pi/2}[/itex] to [itex]\theta= \sqrt{\pi}[/itex]. With [itex]x= \theta^2[/itex] they become [itex]x= (\sqrt{\pi/2})^2= \pi/2[/itex] and [itex]x= (\sqrt{\pi})^2= \pi[/itex].